Question

Please Help Quick ASAP Hurry
Use the net to determine the total surface area.
A. 132 cm2
B. 48 cm2
C. 84 cm2
D. 120 cm2

Answer 1

ANSWER:

Given:

• Side of the square = 6cm
• Base of triangle = 6cm
• Height of triangle = 4cm

To Find:

• Total Surface Area of the figure

Solution:

We can see that, the figure consists of 4 triangles and one quadrilateral in between them. We will find the area of them individually and add them to get our answer.

The quadrilateral has all sides equal, so it is a square.

⇒ Area of square = side²

We are given that,

⇒ Side of the square = 6cm

So,

⇒ Area of square = 6²

⇒ Area of square = 36cm² - - - - -(1)

Now, there are 4 triangles.

Each triangle has the sides 5cm, 5cm and 6cm.

So, they all will have the same area.

Hence,

⇒ Area of triangle = ¹/₂ × base × height

Here, base = 6cm and height is 4cm.

So,

⇒ Area of triangle = ¹/₂ × 6 × 4

⇒ Area of triangle = 12cm²

Now, if area of one triangle is 12cm², then

⇒ Area of 4 triangles = (4 × 12)cm²

⇒ Area of 4 triangles = 48cm² - - - - -(2)

Finally,

⇒ Area of complete figure = Area of square + Area of 4 triangles

From (1) & (2),

⇒ Area of complete figure = 36cm² + 48cm²

⇒ Area of complete figure = 84cm²

Hence, total area of the figure is (option c) 84cm².

Formulae Used:

• Area of square = side²
• Area of triangle = ¹/₂ × base × height

Answer 2

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★The sides of square and triangles.

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★Total surface area.

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• Area of a triangle is ½ × base × height.
• Area of a square is (Side)².

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The sides of the uppermost triangle are:-

5 cm, 5 cm , 6cm

Height of the uppermost triangle is 4 cm.

Area of the triangle will be :-

½×base×height

$= \frac{1}{2} \times 6 \times 4$

$= 1 \times 3 \times 4$

$= 12 \: cm {}^{2}$

★ Hence, the area of the uppermost triangle is 12 cm².

• The sides of the other triangles are same as of the uppermost triangle.
• Since, the area will also be the same.

★Hence, the area of the other triangles will also be 12cm².

Given sides of the square = 6cm, 6cm, 6cm, 6cm.

The area of the square is (Side) ².

So, the area of the square here will be (6)²

= 6×6

= 36 cm².

★Hence, the area of the square is 36 cm².

Total surface area will be:-

Sum of the areas of all the triangles + area of the square

= 12 + 12 + 12+ 12 + 36cm

= 84cm²

★Hence, the total surface area is 84cm².